Divi Examples

Example programs written in Divi

Examples

1. Cluster MaxCut

Partitioned QAOA for MaxCut using graph partitioning to solve the MaxCut problem on large, community-structured graphs. This example demonstrates how to split large graphs (e.g., 50 qubits) into smaller, manageable sub-graphs using spectral clustering, allowing for parallel execution of QAOA circuits on smaller quantum processors or simulators.

Key Features:

• Graph partitioning with spectral clustering
• Parallel QAOA execution on sub-graphs
• Comparison of quantum vs. classical results
• Support for both local simulation and remote execution via QoroService

2. Minimum Birkhoff Decomposition

VQE-based approach to find the Birkhoff decomposition of doubly stochastic matrices. This example showcases the modular design of the divi library, implementing a sophisticated application by inheriting from the VQE class with minimal, targeted changes.

Key Features:

• Custom VQE implementation for Birkhoff decomposition
• Multi-threaded classical optimization with caching
• Command-line interface for various problem configurations
• Support for sparse and dense matrix types

3. Portfolio Optimization

Quantum portfolio optimization using QAOA combined with spectral partitioning to handle large-scale problems. The approach partitions the asset correlation graph into smaller sub-problems that can be solved efficiently on quantum hardware.

Key Features:

• QUBO formulation for portfolio optimization
• Spectral partitioning based on asset correlations
• Interactive Jupyter notebook workflow
• Solution comparison between QAOA and exact solvers
• Comprehensive visualization and financial metrics analysis

4. Quantum-Guided Cluster Algorithm

Implementation of the Quantum-Guided Cluster Algorithm from arXiv:2508.10656. QAOA is run once to extract two-point correlations ⟨Z_i Z_j⟩, which then guide a classical cluster Monte Carlo for Max-Cut — combining quantum insight with efficient classical post-processing.

Key Features:

• QAOA as a one-shot correlation oracle for combinatorial optimization
• QWC observable grouping for efficient correlation measurement (up to 60% circuit reduction)
• Correlation-guided cluster Monte Carlo (Algorithm 1 from the paper)
• Benchmarks against simulated annealing and coupling-constant baselines
• Publication-quality dark-themed visualizations
• Support for cloud execution via QoroService for >18-qubit instances